Question

Suppose that a researcher is planning a new study on hemoglobin levels amongst women under 25 years old. Previous research suggest that the standard deviation of hemoglobin is 0.7 g/dl. In the new study the research wants to have the standard error for the sample mean to be no more than 0.05 g/dl. Find the required sample size for the new study.

Answer 1

A sample size of at least 531 is required.

Explanation:

We are lacking the confidence level to solve this question, so i am going to use a 90% confidence level.

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.9)/(2) = 0.05`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.05 = 0.95`, so
`z = 1.645`

Now, find the margin of error M as such

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

Find the required sample size for the new study.

A sample size of at least n is required.

n is found when
`M = 0.05`

We have that
`\sigma = 0.7`

So

`M = z*(\sigma)/(√(n))`

`0.05 = 1.645*(0.7)/(√(n))`

`0.05√(n) = 1.645*0.7`

`√(n) = (1.645*0.7)/(0.05)`

`(√(n))^(2) = ((1.645*0.7)/(0.05))^(2)`

`n = 530.4`

Rounding up

A sample size of at least 531 is required.